You don’t need to worry about Japanese developers when it comes to creating an insane, over-the-top frenzy on the screen. It is just in their veins; their only barrier is having the necessary game hardware to show it up right.
Just think about the superb 60 frame per sec action in Bayonetta or having 12 characters on the screen all at once in Guardian Heroes (thank you Sega Saturn), there are only a few cooler things than Japanese video games with a crazy amount of chaos.
Bangai-O Spirits

Blowing up everything on the screen at once continously is not an issue in Treasure’s 2008 mecha shooter for the Nintendo DS.
Ultimate Marvel vs. Capcom 3

The combat animations, crazy combos and called-in assists create an ridiculously cool chaos on screen in Capcom’s crossover fighting game.
Gungrave

Superb third-person shooter for the PlayStation 2 in which we control an undead protagonist going after those who killed him.
ESPGaluda

ESPGaluda is one of the many crazy manic shooters from Cave. The arrange mode that changes gameplay rules was added to the PlayStation 2 port in 2004, making it much harder and chaotic.
Crazy Taxi

There are no rules in Sega’s arcade racer, which promotes taxi driving to one of the most enjoyable jobs in the world.
Mushihime-sama Futari

Another bullet hell shooter from Cave, released in 2006, and with its ultra difficulty mode, it’s also among the hardest.
Guardian Heroes

One of the crown jewels of the beat ’em up genre and the Sega Saturn. Six players could play simultaneously making it up to twelve on screen at once, creating a hell of a mess.
Bayonetta

Platinum Games’ fast paced third-person action game tops most of the titles of this genre with its complex, awesome looking combat system and with its difficulty done right. Also, it’s a great thing that Platinum Games stayed on this route with Vanquish and Metal Gear Rising. Fingers crossed for Bayonetta 2.
DoDonPachi Dai Ou Jou

Fourth entry in the DoDonPachi series from Cave, this bullet hell shooter is just insane-super-crazy with impossible situations.
R-Type III

Released in 1993 for the SNES, Irem’s shooter proved that horizontal scrolling shooters also can be insanely hard and awesome with fast paced action messing up the screen.
Sources: Nereid0, JonGodGames, SEGA, Capcom, CAVE, Guardian Heroes Remix, Bayonetta Wiki, Nautth, Naka Teleeli
Parodius needs to be on the list.
Konami mascots flying around fighting giant Maoi (Easter Island) Heads and dozens of other weird aliens, including an indestructable Las Vegas show girl and armies of penguins, set to classic music and seizure inducing lighting effects.
https://en.wikipedia.org/wiki/Parodius_%28series%29
Hey! I got Gaurdian Heroes at half off some time ago, anyone else have that?
Asura’s Wrath, people!
YES
Vanquish, GOD HAND
I think you missed out a lot of Suda 51 games.
Bujingai – Korean though…..
Wasn’t Marvel v Capcom 3 – capcom US?